The morphism \({\check{C}}{{U}}_0 = \coprod _{a \in A} \underline{U}_a \longrightarrow \underline{M}\)  is a local epimorphism, or generalised cover (in the sense of [1]}) with respect to the Grothendieck topology of differentiably good open coverings on \({{C}\mathrm {art}}\)  [2]}, [3]}.
Hence, the result follows from [1]}.
